In the mouths of most directors it would sound like revisionism but when Sam Taylor-Wood describes her debut feature film as "just the most serendipitous shoot", she's completely convincing.

"Every day I felt was just magical," she says, very quietly and calmly in her surprisingly old-fashioned-posh voice. "And considering I was getting up at four in the morning for nine weeks…"

Of course, I might be mistaking calm for exhaustion (she admits she's "totally knackered") but the making of her film – a moving story of the teenage John Lennon's relationships with his glamorous, emotionally fragile mother (Anne-Marie Duff) and his stern, disciplined Aunt Mimi (Kristin Scott Thomas) – does seem to have gone smoothly from the very beginning.

The director Joe Wright, a friend of hers, pilfered Matt Greenhalgh's script (based on a memoir by Julia Baird, Lennon's half-sister) from his agent's desk because, as she reports him saying, "my sensibility was written all over it and I'd know what to do with it". She read it in one go on a train journey back from Devon, a "desperate dribbling wreck" by the time she'd finished. "It was just an earth-shattering read, it was one of those stories that just rocks your foundations. It's a great experience and a very rare one – I've not had it before." She's not one to overstate the parallels between her own young life and Lennon's (both were abandoned by their mothers at the age of five) but simply says, "I suppose I had a sense of understanding of abandonment – it was there and I understood it."

But how to begin making a film about perhaps the most mythologised musical icon we have?

"I tried to stay with the script and not get too caught up in the millions and millions of biographies because they all contradict one another – everyone claiming that they gave Lennon his first guitar or this, that and the other." She did read Pete Shotton's memoir and Philip Norman's biography, "but I tried to focus on it as a coming-of-age story rather than a film about a great icon". And once they were on set, "every time it did become a bit nerve-racking I'd just have a cup of tea and go read the script to focus on the story." She also listened to rock'n'roll pretty much constantly – "a lot of Elvis and Ike Turner and Buddy Holly – people had been growing up with "innocent" music and then suddenly there was this – it's quite hard for us to take that on board."

When I ask if she remembers her first day of filming she laughs, "Yeah, I can never forget that, it was pretty extraordinary." She decided to begin with the trickiest scene there was to shoot: one in which Lennon and his best friend Pete Shotton ride on the roof of a double decker bus through Liverpool. She explains: "It was so technologically complicated that it didn't give me a chance to focus on my nerves, all I was thinking of was the logistics of how the hell to make it work. We had all weather that day: rain, snow, hailstones and sunshine. It was also scary because I had Aaron [Johnson, who plays Lennon] and Josh Bolt who plays Pete Shotton, so make one mistake and I've lost the two main actors of the film."

Finding Johnson for that lead role was typically serendipitous. He was the eighth or ninth actor she saw from a list of around 300 but, "I knew the moment he came in. He just had the right intensity, mannerisms, I dunno, everything, it all clicked into place." That "clicking into place", as everyone now knows, was romantic as well as artistic: in October she announced her engagement to her film's 19-year-old star. In terms of Lennon's real-life lover though, the course of things may not have run as smooth: his widow Yoko Ono owns the rights to "Mother", the song that Taylor-Wood says "finally finished me off" when she read it at the script's end; to her its inclusion was "essential". It depended though, on Ono's reaction to the film. She watched it in a private screening in New York while Taylor-Wood held her breath the other side of the Atlantic. "She's obviously very protective of Lennon – she's never given the rights before – but I just quietly held this belief that she would like it." She did. Since then Ono has publicly praised the film which, Taylor-Wood says, "is worth its weight in gold on an emotional level. She was incredibly moved by it and thought the essence and spirit of Lennon was completely there."

Has her own idea of the essence of Lennon changed after being so immersed in his life? Her answer is characteristically tranquil: "I got a much closer sense of him and a much stronger affinity with him. It was quite a soulful experience I guess." There's a pause. "You do start sounding a bit sort of spiritual," she apologises, "but then, he was."